{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Statistics Seminar\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from thinkbayes2 import Suite\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian bandits\n",
    "\n",
    "\n",
    "Here's a definition for `Bandit`, which extends `Suite` and defines a likelihood function that computes the probability of the data (win or lose) for a given value of `x` (the probability of win).\n",
    "\n",
    "Note that `hypo` is in the range 0 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Bandit(Suite):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\" \n",
    "        hypo is the prob of win (0-100)\n",
    "        data is a string, either 'W' or 'L'\n",
    "        \"\"\"\n",
    "        x = hypo / 100\n",
    "        if data == 'W':\n",
    "            return x\n",
    "        else:\n",
    "            return 1-x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start with a uniform distribution from 0 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TBo4kqQkDR5LUhIEjSWrCwJEkNWHgSJKaMHAkSU0YOJKkJgwcSVITBo4kqQkDR5LUhIEj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\nMeViAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5bfafd290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit = Bandit(range(101))\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can update with a single loss:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ULCKl53xmNpO/WM7XCzZQ8F9Vp+ua8lRqMvVrV/OtNyldChYPChaR0rdp+34m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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5bd621510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit.Update('L')\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another loss:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GAA8RCrEn3f1+MxtH6Mjl8XCfScAIQhNe3uzuS8LtzwPZQBMgD7jX3Z82s8bA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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5bd674fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit.Update('L')\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a win:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mQkRJEySXeP+dhWdtsEPAQWC+95gpxIr1Ozh+8gwA1auUtyVcTMSpX6sKt1/b\nwylPmrGMjVuLHJxpooy/y+YPBjYBr+JZomWjdykWU4g5Szc6zy/r3MyWcDER6dqU9s6XplxV/vXh\nTDKzsl2OyoQCf8cJvgj0VdUUVe0D9AX+GbywwteZzCwWrtzilK0bzEQqz3bGfUlM8Gwiu2PPISZM\nXexyVCYU+JtYjqnqRp/yz8CxIMQT9n5as40zmVkA1K1ZmSYNbLSMiVx1alTiruudaWdM/mEF637e\n7WJEJhSUNCrsJhG5CfhJRKaKyD0icjfwFWBfTQox17cbrIt1g5nIN+DyNnRokQR41lZ6bfxM58uV\niU4lXbFc532UAfYAfYAUYB9QNqiRhaETp87kW8n4Ctt+2EQBEWHUsD6ULZMAwK59R/hwyiKXozJu\nKmmtsOHF/dzkt2jlFmc8f6P6NZwVYY2JdDWrVWT4jZfyn488g0W/nrWKHh0a07ZZPZcjM27wd1RY\nGRH5rYj8R0TePfsIdnDhxnfuymW24KSJMv16tKJLm7w1Z1/7cCanz1iXWDTy9+b9B0AdPLs5zsKz\nArHdvPdx4tQZlq/P21bGVjI20UZEuH9oH8p5u8T2HjzG+1/Odzkq4wZ/E0szVf0v4ISqvg8MBnqU\n0Caq/LR6Kzk5ng29GifVoE6NSi5HZEzpq1a5PL+6+XKnPH3uWlas3+FiRMYN/iaWs9ezh0WkHVCZ\nEN610Q2+3WC9OtnViolevbs1p0eHxk753+NncuLUGRcjMqXN38TypohUBf4LmAysxbN0vQFOnspk\n2bq8brBLOzVxMRpj3CUijLj1CiqUSwTgwOETjP18nstRmdLkV2JR1bdV9ZCqzlLVJqpa6+zukgaW\nrNmabzSY7Wtvol2ViuUYcWtvpzxz4Xp+WrPVxYhMafJ3VFh1EfmXiCwVkSUi8rKIVA92cOFi3vJN\nznO7WjHG47LOTfMNYhkzYRbHTpx2MSJTWvztCpuAZ1/5XwA3A/uBj/1pKCIDRWSdiGzwbiNcWJ1X\nRSRdRJaLSKeS2opIRxGZLyLLRGSRiHTz83UE3KnTmSxNs24wYwoz4pYrqFzRM5f60NGTvP3ZHJcj\nMqXB38RSV1X/qqqbvY+/AbVLaiQiMXhWQx4AtAWGiUirAnUGAU1VtTkwEhjjR9vngT+ramfgz8A/\n/HwdAbdkzTanG6xh3WrUr1XFrVCMCTkVy5fhN7/s45TnLNmYb6CLiUz+JpbpIjJURGK8j1uBaX60\n6w6kq+qV3vAaAAAbqElEQVRWVc3Cc+UzpECdIcA4AFVdCFQWkdoltM3FMzINoAqQ4efrCLj51g1m\nTLG6t29ESveWTvnNibM5cuyUixGZYCtpEcpjInIU+DUwHsj0PiYAI/w4f31gu095h/eYP3WKa/sI\n8IKIbMNz9fKUH7EEXGZWdoFuMBtmbExh7r2pF9Uqlwfg6PFTvPnJj6iqy1GZYClpB8mKqlrJ+2+M\nqsZ5HzGqGqwZgP4sB3w/8LCqNsSTZFxZXmbF+h3Oxkb1alamQR1bG8yYwpQvm8ioYSlOecHKzcxe\nku5eQCaoStrz3iEi1wNnxw+mquoUP5plAA19ykmc222VATQopE5CMW3vVtWHAVT1UxF5p6gARo8e\n7TxPSUkhJSXFj7D9s3DlZue574QwY8y5OrduQP9erZkxLw2AtybOoV3z+s6VjHFPamoqqampATuf\n+HM5KiLPApcAH3oPDQN+UtViu6BEJBZYD1wJ7AIWAcNUNc2nzjXAb1V1sIj0BF5W1Z5FtB2qqutE\nZA0wSlVniciVwLOqekkhv1+Ddbmdk5PLvX9639nb/plHbqRFoxLHMxgT1U6dzuTR5yay96BnqcHO\nrRvwx5HX2L5FIUZEUNUL/o/i7837a4D+qvquqr4LDMSzXlixVDUHeACYDqwBJqhqmoiMFJER3jpT\ngc0ishF4AxhVTNt13lP/GnhRRJYBf8O/+z0BtW7zbiepVK1UjubJtsKNMSUpWyaBB27v6/R3L0vb\nzvcL1hXbxoQfv7vC8Iy+Ouh97vfUclX9FmhZ4NgbBcoP+NvWe3we4NrcFfDsvXLWJe0b2TcuY/zU\ntlk9BvfpwJRZKwF4d9I8OrRMola1ii5HZgLF3yuWZ4BlIvKeiLwPLAH+HrywQpuq2v0VYy7C7dd1\np5536aMzmVn86/9+sFFiEaTExCKer+JzgJ7AJOAz4FJV9WvmfSTauvMA+w55+ojLlkmgne2SZ8x5\nSYiP46E7+zldYms37WJK6ipXYzKBU2Ji8d79nqqqu1R1svexuxRiC1kLfbrBurRpSFxcrHvBGBOm\nmifX5qb+XZzyh1MWsmPPIRcjMoHib1fYUhE5Z9RVtFq0aovz3LrBjLlwtw7sSqP6NQDIys7h1Q9+\ncDbMM+HL38TSA1ggIptEZKWIrBKRlcEMLFTtPXiMLRn7AYiNjaFL6wYltDDGFCUuLpaH7uhLbKzn\no2jT9n18NmOpy1GZi+VvYhkANAH6AdcB13r/jTo/rd7iPO/Qoj5lvft7G2MuTHK96gwdlNchMnHa\nUjZt2+diROZilbRWWBkR+R3wOJ65KxneRSG3qmpU7tqzZM0253m3to3cC8SYCHLDlR1p2bgOALm5\nubz6fz84yyWZ8FPSFcv7eOaLrAIGAS8GPaIQdup0JqvS81ak6dq2YTG1jTH+iomJ4cHb+5KYEA/A\njj2H+PCrRS5HZS5USYmljare4Z3QeDNwRSnEFLJWrN/h3FhsWLcaNW1ClzEBU7dmZe654VKnPGXW\nSlZtcG1HDHMRSkosWWefqGrUX5f67tl9SbtG7gViTITq36s1nX0GxLw2fiYnTp1xMSJzIUpKLB1F\n5Kj3cQzocPa5d5+WqKGq+e+vtEt2MRpjIpOIMGpYChXKJQKw/9Bx3p00z+WozPkqaT+WWO9+LGf3\nZInzeR6s/VhCUvrWvRw97tn1rlKFsrbopDFBUq1yeUbc2tsppy5ab9sZhxl/hxtHvSU+3WBd2za0\nRSeNCaLLOjfliq7NnfKYj2dx8MgJFyMy58MSi58Wr/ZJLG2sG8yYYPv1LZdTvYpnE7DjJ8/wn49S\nbaHKMGGJxQ/7Dx1n684DgGe2fadWSS5HZEzkK182kQdv7+eUl6VtZ9qctS5GZPxlicUPvt1g7ZrV\ns9n2xpSS9i3qc11KB6f83hfzbKHKMBD0xCIiA0VknYhsEJEniqjzqoiki8hyEenkT1sReVBE0rzr\nlj0bzNewdG3eaLCuba0bzJjSdNu13WlQtxrgWajy5XHfk52d43JUpjhBTSwiEgO8hmetsbbAMBFp\nVaDOIKCpqjYHRgJjSmorIil41iprr6rtgReC9RqysnJYlb7TKXdpY7PtjSlNCfFxPHLXlc5ClZt3\n7Ofjb35yOSpTnGBfsXQH0r1ri2UBE4AhBeoMAcYBqOpCoLKI1C6h7f3As2cnbarq/mC9gLU/7+JM\npmeeaJ0alahb0+9dmY0xAZJcrzp3XNfDKX/+3TLWbtrlYkSmOMFOLPWB7T7lHd5j/tQprm0LoLeI\nLBCRmSLSLaBR+1jm0w1mVyvGuOe6lA60b+H5CFDglQ++t1n5ISrO7QAK4c8EkTigqqr29G5A9gme\nZf3PMXr0aOd5SkoKKSkp5xXMsrS83Na5tSUWY9wiIjxwW18efW4iJ06dYf+h47zxyWweuetKm1d2\nkVJTU0lNTQ3Y+YKdWDIA30/jJO+xgnUaFFInoZi2O4BJAKq6WERyRaS6qh4oGIBvYjlfew8ec0ag\nxMXF0rZZ3Qs+lzHm4tWoWoHfDO3Ni2NnADB36Ua6tmlIn0tauBxZeCv4pfsvf/nLRZ0v2F1hi4Fm\nIpIsIgnAUGBygTqTgbsARKQncFhV95TQ9gs8m44hIi2A+MKSysXy7QZr16yes6S3McY9vTo1pV+P\nvDFAb06cze79UbV0YcgLamJR1RzgAWA6sAaYoKppIjJSREZ460wFNovIRuANYFRxbb2nfhdoIiKr\ngPF4E1Og5e8Gsy2IjQkV9/3iMmcgzekzWbzywffOlhbGfRLJSySIiF7o68vKyuHup99zRoS9+seh\n1K9VJZDhGWMuwsate3nq5S/IzfUklJsHdGXYNZeU0Mr4Q0RQ1Qu+cWUz74uQ5jPMuHb1StSzYcbG\nhJRmybXyJZLPpi1hzcadxbQwpcUSSxEKdoPZqBNjQs8NV3akXfN6QN4Q5GMnTrsblLHEUpRl63wS\ni81fMSYkxcTE8NAd/ZyNwQ4cPmGrIIcASyyFOHjkBNt3HQQ8qxm3a1bP5YiMMUWpXqUCD9ze1ykv\nWrXFVkF2mSWWQqxYt8N53rpJHcok2jBjY0LZJe0acU3vdk557Bfz2JIRtJWeTAkssRRi+fq8brCO\nLW2YsTHh4M7re9LQuwpydnYOL46dwekzWS5HFZ0ssRSgqqxcn7c4gG3qZUx4SIiP47Hh/UmI9ywo\nsnPfEd6cONvlqKKTJZYCtmQc4OjxUwBULF+Gxkk1XI7IGOOvpNpVGXHLFU551uINzFy43sWIopMl\nlgKW+4wG69AyyYYZGxNm+vZomW/tsDcnzmb7btt1sjRZYilgxfq8G/edWlo3mDHhaMQtVziTmjOz\nsnnxvRnOhGcTfJZYfJzJzMq3eVAHSyzGhKUyifH8/t6riY+LBWD7roO89ekcl6OKHpZYfKzdtNtZ\nyC6pdlVqVK3gckTGmAuVXK86v7r5cqc8c+F6u99SSiyx+Fjhc3+lo40GMybsXdmzFb27NXfKb3zy\nI1t3HnQxouhgicXHcp/7Kx2tG8yYsCcijLy1N0m1qwKQlZ3DC+9O4+SpTJcji2yWWLwKLuPS1pZx\nMSYilEmMP2d+y79tPbGgssTitWpD3qTIlo1q2zIuxkSQhnWrcf/Q3k55wYqfmZK6ysWIIlvQE4uI\nDBSRdSKyQUSeKKLOqyKSLiLLRaSTv21F5DHvfvfVLjbOlT6JpX2L+hd7OmNMiOndrQUDL2/rlMdN\nXkCazyhQEzhBTSwiEgO8BgwA2gLDRKRVgTqDgKaq2hwYCYzxp62IJAH9ga0XG6eqsjo9L7F0aGH3\nV4yJRPfc0IvmybUAyM3N5YWxMzh45ITLUUWeYF+xdAfSVXWrqmYBE4AhBeoMAcYBqOpCoLKI1Paj\n7T+BxwMR5O79R9l/6DgAiQnxNGtYMxCnNcaEmPj4WH4//Gpn/5bDx07ywtgZZGfnuBxZZAl2YqkP\nbPcp7/Ae86dOkW1F5Hpgu6oGpJPU9/5K22Z1ifNOqjLGRJ4aVSvw6D39ObtY0/rNu3l30jxXY4o0\ncW4HUIhiF+cSkbLA03i6wUpsM3r0aOd5SkoKKSkp59Sx+yvGRJeOLZO44/qefDB5AQDT5q6heXIt\n+vZo6XJk7khNTSU1NTVg5wt2YskAfPf1TfIeK1inQSF1Eopo2xRoBKwQzwqRScASEemuqnsLBuCb\nWApz7v0VSyzGRIMh/Tqycds+5i/fBMCYT36kQZ2qNPPeg4kmBb90/+Uvf7mo8wW7K2wx0ExEkkUk\nARgKTC5QZzJwF4CI9AQOq+qeotqq6mpVraOqTVS1MZ4uss6FJRV/bN15gGMnTgOeZfKT61W/kNMY\nY8KMiPDAbSk08Nkc7Nm3v7Wb+QEQ1MSiqjnAA8B0YA0wQVXTRGSkiIzw1pkKbBaRjcAbwKji2hb2\nayih+6w4qzbsdJ63a17flsk3JoqUSYznifsGUL6s52b+oaMnef6daWRl2c38iyGRPPtURLSk1/e/\nb3zDkrWeEcsjb+3N1Ze1KY3QjDEhZMX6Hfz1P1M4+2nRt0dLfjssJWq/aIoIqnrBLz6qZ95nZ+ew\neqPvFYst42JMNOrYMom7b+jllGcuXG8z8y9CVCeWTdv3OZv/VK9SnrrejYGMMdHn2pT2pHTPGxX2\n/hfz+GnNRc+/jkpRnVhWpeddrbRvYdsQGxPNPCshX0HLxnUAz83bl977jq07D7gbWBiK6sSyxjex\nWDeYMVEvIT6OJ+4bQM2qFQHPrrLPvPkth4+ddDmy8BK1iSU7O4e0n/MWoLNl8o0xAJUrluWpEYOc\nFc73HTrGs299S2ZWtsuRhY+oTSwbt+0jy7s+UO3qlahZraLLERljQkVyvWo8evdVzjyG9K17eWXc\n9+Tm5roaV7iI2sTiOxrMrlaMMQV1bZvM8Jsuc8oLVm7m/S8WuBhR+IjaxOJ7f8WGGRtjCjO4T3uu\n7dPBKU+ZtZKvZ9kw5JJEZWIpeH+lTdO6LkZjjAlld9/Qkx4dGjvlsZPmMs+7vpgpXFQmFt/7K7Wq\nVbT7K8aYIsXExPDwnf2cDcIUeHnc9/kWrzX5RWViyXd/xbrBjDElSEyI56lfD3ImUefk5PLs29PY\nkrHf5chCU1Qmlnz3V+zGvTHGD5UrluW/R11L1UrlADh1OpO/vj6VPQeOuhxZ6Im6xJKdncO6zbud\nchtLLMYYP9WqVpH/un8w5cokAJ6tjf/y7ym21H4BUZdYNm7b50x0qlWtIrXs/oox5jwk16vOk78e\n6GxhvufAUf7y7ykcPX7K5chCR9QlFru/Yoy5WG2b1ePxe68mJsbzEbpjzyH+5/WvOXHqjMuRhYao\nSyx2f8UYEwjd2ibz8J39nNn5m3fs5+9vfMOp05muxhUKgp5YRGSgiKwTkQ0i8kQRdV4VkXQRWS4i\nnUpqKyLPi0iat/5nIlLJn1hycnJZv2WPU7b7K8aYi3F5l2bcP6yPU16/eTd/f+MbTp/JcjEq9wU1\nsYhIDPAaMABoCwwTkVYF6gwCmqpqc2AkMMaPttOBtqraCUgHnvInns079jv7r9SoWsHurxhjLtqV\nPVtzr8/SL2k/7+Lvb0yN6uQS7CuW7kC6qm5V1SxgAjCkQJ0hwDgAVV0IVBaR2sW1VdXvVPXsanAL\ngCR/glmzKW+2fesmNtveGBMYg/u05x6fHSjXbtrF/74ZvVcuwU4s9YHtPuUd3mP+1PGnLcC9wDf+\nBJO2yZZxMcYEx3V9O3DXkEud8pqNO6P2hn6c2wEUwu9tHEXkj0CWqo4vqs7o0aMBUFUWpJ+mQk3P\nmj+tLbEYYwJsSL+OqCofTPasgrx+825G/3sK/33/YCqWL+NydEVLTU0lNTU1YOcTVQ3Yyc45uUhP\nYLSqDvSWnwRUVZ/zqTMGmKmqH3vL64A+QOPi2orIPcCvgX6qWuhXAhHRs69v++5D/O6ZjwGoWL4M\nY/9+t21FbIwJiimpKxn7+Tyn3KBuNf7sM2s/1IkIqnrBH5DB7gpbDDQTkWQRSQCGApML1JkM3AVO\nIjqsqnuKaysiA4HHgeuLSioFrfWZv9K6SR1LKsaYoLk2pQO/+WVvp/tl+66D/PHlL9i174ircZWW\noCYWVc0BHsAzimsNMEFV00RkpIiM8NaZCmwWkY3AG8Co4tp6T/0voAIwQ0SWish/Soplrc8y+dYN\nZowJtv692vDgHf2I8X6J3XPgKE+//AWbtu1zObLgC2pXmNt8u8JG/PkDDhz2rOfz3KM30cy7BLYx\nxgTTolVbeOm9Gc5WHYkJ8TzxqwF0bOnXYFZXhHpXWEjYe/CYk1QSE+JpnFTD5YiMMdGie/tGjP7t\ndZQvmwjAmcws/jZmKjPmrXU5suCJisTiO8y4ZaPaxMZGxcs2xoSIVk3q8Pff3UD1KuUByM3NZczH\nP/Le5/PIzc0toXX4iYpP2LW+EyOb1nExEmNMtGpQpyrPPHIjjern9Zh8lbqS596exslTkbW+WFQk\nFpsYaYwJBdWrVODvDw+he/tGzrGf1mzlyZcmsX33IfcCC7CITyxHjp0iY+9hAGJjY2jRqLbLERlj\nolmZxHj+cN8AhvTr6BzL2HuYJ16cxPzlP7sYWeBEfGLx3S2yaYOaJMSH4mIDxphoIiLcNeRSHr6z\nH/HeDcPOZGbxwtjpjJ00j6ysHJcjvDgRn1jW+ySWVo3t/ooxJnT07taC5x67idrV83b+mDJrJU/+\n83OnpyUcRXxiWbc5b/+VVk0ssRhjQktyveo8//tf0K1tsnNsS8Z+fv/8p8yYt5ZwnGsY8Yll47a9\nznO7YjHGhKIK5RJ58tcDufemy4jzdo1lZmUz5uMf+evrX7P34DGXIzw/EZ9YcnI8Y8Tr1qxM5Ypl\nXY7GGGMKJyIM7tOe5x69kfq1qjjHV6zfwe+e+YRvZ68Jm6uXiE8sZ7W0qxVjTBhoVL8G/3j8F1yX\n0sFZxPJMZhZvfTqbJ16cxAaf7dVDVdQkllaNbZixMSY8JCbEc8+NvfjfR/JfvWzavo+n/vk5r42f\nycEjJ1yMsHjRk1hsK2JjTJhp0ag2L/zhZm4e0NW59wIwc+F6Rv3PeD6YvIBjJ067GGHhIn5145se\nep3yZRN5/5l7bA8WY0zY2r3/KO99Po/Fq7fkO162TAKDe7djUO92VKkYmI3ELnZ146hILF3bJPP0\nyEFuh2OMMRdt+brtfDB5IVsy9uc7HhcXS++uzbmubwca1q12Ub8j5JfNF5GBIrJORDaIyBNF1HlV\nRNJFZLmIdCqprYhUFZHpIrJeRKaJSOXiYmjZxO6vGGMiQ6dWDXjh8V/w2PD++e6/ZGfn8MPCdTzy\n7Cc8+dIkvp29huMn/dpgN+CCmlhEJAZ4DRgAtAWGiUirAnUGAU1VtTkwEhjjR9snge9UtSXwA/BU\ncXHY/BVITU11O4SQYe9FHnsv8oTTeyEi9OrUlJefupVH7+lP8wIbF6Zv3ctbn87m3j+9z9/GfM3U\nH1eV6lyYYC+c1R1IV9WtACIyARgCrPOpMwQYB6CqC0WksojUBhoX03YI0Mfb/n0gFU+yOUdMTAzN\nGtYM8MsKP6mpqaSkpLgdRkiw9yKPvRd5wvG9iImJ4bLOTenVqQnrN+/hq9SVLF69xZm/l5OTy7K0\n7SxL2847n82lVrWKNG9Um+YNa9GkQQ1qV69E9SrlA37/OdiJpT6w3ae8A0+yKalO/RLa1lbVPQCq\nultEitxnuElSDRIT4i8semOMCQMiQqsmdWjVpA7HTpxm9pJ0UhdtYNP2ffnq7T14jL0HjzF36Ubn\nWGxsDDWrVqBMYgJlEuMom3jxn5ehuNTvhaTOIkcgWDeYMSaaVCxfhmt6t+ea3u3Ze/AYS9ds46c1\nW1idvpOs7HNXTc7JyWX3/qOBDUJVg/YAegLf+pSfBJ4oUGcM8Euf8jqgdnFtgTQ8Vy0AdYC0In6/\n2sMe9rCHPc7/cTGf/cG+YlkMNBORZGAXMBQYVqDOZOC3wMci0hM4rKp7RGR/MW0nA/cAzwF3A18W\n9ssvZricMcaYCxPUxKKqOSLyADAdzwi0d1Q1TURGen6sb6rqVBG5RkQ2AieA4cW19Z76OeATEbkX\n2ArcGszXYYwxxn8RPUHSGGNM6YvItcL8mZQZqUQkSUR+EJE1IrJKRB7yHj+vSaWRRERiRGSpiEz2\nlqPyvfAO5Z8oImnev48eUfxePCIiq0VkpYh8KCIJ0fJeiMg7IrJHRFb6HCvytYvIU94J7GkicrU/\nvyPiEos/kzIjXDbwqKq2BS4Ffut9/ec1qTTCPAys9SlH63vxCjBVVVsDHfEMlIm690JE6gEPAl1U\ntQOeWwLDiJ73Yiyez0dfhb52EWmD51ZDa2AQ8B/xY9JLxCUWfCZlqmoWcHZiZVRQ1d2qutz7/Die\nEXRJeN6D973V3gducCfC0iUiScA1wNs+h6PuvRCRSsAVqjoWQFWzVfUIUfheeMUC5UUkDigLZBAl\n74WqzgEOFThc1Gu/Hpjg/XvZAqRz7lzEc0RiYilqwmXUEZFGQCdgAQUmlQJFTiqNMP8EHsczhPKs\naHwvGgP7RWSst1vwTREpRxS+F6q6E3gR2IYnoRxR1e+IwvfCR60iXnvBz9MM/Pg8jcTEYgARqQB8\nCjzsvXIpOEoj4kdtiMhgYI/3Cq64y/eIfy/wdPd0Af6tql3wjMB8kuj8u6iC5xt6MlAPz5XL7UTh\ne1GMi3rtkZhYMoCGPuUk77Go4b28/xT4QFXPzvHZ412DDRGpA+x1K75SdBlwvYj8DHwE9BORD4Dd\nUfhe7AC2q+pP3vJneBJNNP5dXAX8rKoHVTUH+BzoRXS+F2cV9dozgAY+9fz6PI3ExOJMyhSRBDwT\nKye7HFNpexdYq6qv+Bw7O6kUiplUGklU9WlVbaiqTfD8HfygqncCXxF978UeYLuItPAeuhJYQxT+\nXeDpAuspImW8N6KvxDO4I5reCyH/VXxRr30yMNQ7aq4x0AxYVOLJI3Eei4gMxDMC5uzEymddDqnU\niMhlwI/AKvKWZ3gazx/DJ3i+fWwFblXVw27FWdpEpA/wmKpeLyLViML3QkQ64hnEEA/8jGcycizR\n+V78Gc+XjSxgGfAroCJR8F6IyHggBagO7AH+DHwBTKSQ1y4iTwH34XmvHlbV6SX+jkhMLMYYY9wT\niV1hxhhjXGSJxRhjTEBZYjHGGBNQlliMMcYElCUWY4wxAWWJxRhjTEBZYjHGGBNQlliMMcYElCUW\nY0qRiHQTkRXeJTLKezebauN2XMYEks28N6aUicj/4NkDpCyehSGfczkkYwLKEosxpUxE4vEslnoK\n6KX2P6GJMNYVZkzpqwFUwLPoYRmXYzEm4OyKxZhSJiJf4tkfpjFQT1UfdDkkYwIqzu0AjIkmInIn\nkKmqE0QkBpgrIimqmupyaMYEjF2xGGOMCSi7x2KMMSagLLEYY4wJKEssxhhjAsoSizHGmICyxGKM\nMSagLLEYY4wJKEssxhhjAsoSizHGmID6fyPIiqCnB2JFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5bd2cc510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit.Update('W')\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting over, here's what it looks like after 1 win and 9 losses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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H10xDmvvGqjRG45xrquImFkV6t98CJgDPAs8Al5hZQjPvmxqfdd8wUy4fSfWN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\n/w+y6Slh3TwqjgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5f0113350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bandit = Bandit(range(101))\n",
    "\n",
    "for outcome in 'LLWLLLLLLL':\n",
    "    bandit.Update(outcome)\n",
    "\n",
    "thinkplot.Pdf(bandit)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')\n",
    "bandit.MaximumLikelihood()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior mean is about 17%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16.68194469884906"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bandit.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most likely value is the observed proportion 1/10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bandit.MaximumLikelihood()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior credible interval has a 90% chance of containing the true value (provided that the prior distribution truly represents our background knowledge)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 36)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bandit.CredibleInterval(90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian A/B testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose we have several bandits and we want to decide which one to play."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example, suppose we have 4 machines with these probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "actual_probs = [10, 20, 30, 40]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function simulates playing one machine once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from random import random\n",
    "from collections import Counter\n",
    "\n",
    "counter = Counter()\n",
    "\n",
    "def flip(p):\n",
    "    \"\"\"Returns True with probablity `p`, False otherwise.\n",
    "    \n",
    "    p: float probability\n",
    "    \n",
    "    returns: boolean\n",
    "    \"\"\"\n",
    "    return random() < p\n",
    "\n",
    "def play(i):\n",
    "    \"\"\"Plays the `i`th machine and returns the outcome.\n",
    "    \n",
    "    i: integer index into `actual_probs`\n",
    "    \"\"\"\n",
    "    counter[i] += 1\n",
    "    p = actual_probs[i] / 100\n",
    "    if flip(p):\n",
    "        return 'W'\n",
    "    else:\n",
    "        return 'L'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a test, playing Machine 3 twenty times:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L W W L L L W W W W W L L L W L W L L L "
     ]
    }
   ],
   "source": [
    "for i in range(20):\n",
    "    result = play(3)\n",
    "    print(result, end=' ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 1** Create a `Bandit` object to represent your beliefs about Machine 3.  Write a loop that plays Machine 3 20 times and updates your beliefs based on the outcome.  Plot the posterior distribution of `x` and the 90% credible interval.  Does the CI contain the actual probability for Machine 3, which is 30%?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## STOP HERE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The strategy\n",
    "\n",
    "Now I'll make 4 `Bandit` objects to represent our beliefs about the 4 machines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "prior = range(101)\n",
    "beliefs = [Bandit(prior) for i in range(4)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The core of the Bayesian Bandits Strategy is this process for choosing which machine to play:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def choose(beliefs):\n",
    "    \"\"\"Chooses a machine in proportion to its probability of superiority.\n",
    "    \n",
    "    beliefs: list of Bandit objects.\n",
    "    \n",
    "    returns: integer index of the chosen machine.\n",
    "    \"\"\"\n",
    "    ps = [b.Random() for b in beliefs]\n",
    "    return np.argmax(ps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It chooses a random value from each posterior and returns the index of the machine with this highest generated value of `x`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "choose(beliefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function updates our beliefs about one of the machines based on one outcome."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def update(beliefs, i, outcome):\n",
    "    \"\"\"Updates Machine `i` based on `outcome`.\n",
    "    \n",
    "    beliefs: list of Bandit objects.\n",
    "    i: index integet into beliefs\n",
    "    outcome: string, either 'W' or 'L'\n",
    "    \"\"\"\n",
    "    beliefs[i].Update(outcome)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2**  Fill in this function to use `choose` to pick a machine, `play` to play it, and `update` to update our beliefs about the chosen machine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def choose_play_update(beliefs, verbose=False):\n",
    "    \"\"\"Chooses a machine, plays it, and updates `beliefs`.\n",
    "    \n",
    "    If `verbose`, print the index of the chosen machine, `i`,\n",
    "    and the `outcome`.\n",
    "    \n",
    "    beliefs: list of Bandit objects.\n",
    "    verbose: boolean\n",
    "    \"\"\"\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test your method here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "counter = Counter()\n",
    "choose_play_update(beliefs, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing the bandit strategy\n",
    "\n",
    "Start with a fresh batch of `Bandit` objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "prior = range(101)\n",
    "beliefs = [Bandit(prior) for i in range(4)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And reset the counter that keeps track of how many times we play each machine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "counter = Counter()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function displays the four distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "options = dict(yticklabels='invisible')\n",
    "\n",
    "def plot(beliefs):\n",
    "    thinkplot.preplot(rows=2, cols=2)\n",
    "    for i, b in enumerate(beliefs):\n",
    "        thinkplot.subplot(i+1)\n",
    "        thinkplot.Pdf(b, label=i)\n",
    "        thinkplot.config(**options)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XjrwnCeZh3759qaq1eNu3b9+i/ziBU2xddth27i/3JMFJ2vwuZdFjzMWxzuKeJFhf67LD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5bd0baa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(beliefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can play a few times and see how `beliefs` gets updated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5bcbac310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    choose_play_update(beliefs)\n",
    "    \n",
    "plot(beliefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we play 90 more times, the estimates get better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5bcbe89d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(90):\n",
    "    choose_play_update(beliefs)\n",
    "    \n",
    "plot(beliefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can summarize `beliefs` by printing the posterior means and credible intervals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50.0 (5, 95)\n",
      "50.0 (5, 95)\n",
      "50.0 (5, 95)\n",
      "50.0 (5, 95)\n"
     ]
    }
   ],
   "source": [
    "for i, b in enumerate(beliefs):\n",
    "    print(b.Mean(), b.CredibleInterval(90))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The credible intervals usually contain the true value, but the estimates are still rough, especially for the lower-probability machines.  But that's not the important part.  \n",
    "\n",
    "The goal is to play the high-probability machines most often.  Making the estimates more precise is a means to that end, but not an end itself.\n",
    "\n",
    "Let's see how often we played each machine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for machine, count in sorted(counter.items()):\n",
    "    print(machine, count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise 3** Run another 100 iterations.  How many times do we play the best machine?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}